Model averaging based on weighted generalized method of moments with missing responses

Zhongqi Liang; Yanqiu Zhou; Zhongqi Liang; Yanqiu Zhou

doi:10.3934/math.20231106

AIMS Mathematics

2023, Volume 8, Issue 9: 21683-21699. doi: 10.3934/math.20231106

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Model averaging based on weighted generalized method of moments with missing responses

Zhongqi Liang ^1,2,
Yanqiu Zhou ^{3
,
,}

1.
School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China
2.
School of Computer and Computing Science, Hangzhou City University, Hangzhou 310015, China
3.
School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China

Received: 14 March 2023 Revised: 28 May 2023 Accepted: 31 May 2023 Published: 07 July 2023
MSC : 62F12, 62F99, 62J05

Model averaging based on the least squares estimator or the maximum likelihood estimator has been widely followed, while model averaging based on the generalized method of moments is almost rarely addressed. This paper is concerned with a model averaging method based on the weighted generalized method of moments for missing responses problem. The weight vector for model averaging is obtained via minimizing the leave-one-out cross validation criterion. With some mild conditions, the asymptotic optimality of the proposed method in the sense that it can achieve the lowest squared error asymptotically is proved. Some numerical experiments are conducted to evaluate the proposed method with the existing related ones, and the results suggest that the proposed method performs relatively well.
- asymptotic optimality,
- generalized method of moments,
- missing responses,
- model averaging
Citation: Zhongqi Liang, Yanqiu Zhou. Model averaging based on weighted generalized method of moments with missing responses[J]. AIMS Mathematics, 2023, 8(9): 21683-21699. doi: 10.3934/math.20231106

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Abstract

Model averaging based on the least squares estimator or the maximum likelihood estimator has been widely followed, while model averaging based on the generalized method of moments is almost rarely addressed. This paper is concerned with a model averaging method based on the weighted generalized method of moments for missing responses problem. The weight vector for model averaging is obtained via minimizing the leave-one-out cross validation criterion. With some mild conditions, the asymptotic optimality of the proposed method in the sense that it can achieve the lowest squared error asymptotically is proved. Some numerical experiments are conducted to evaluate the proposed method with the existing related ones, and the results suggest that the proposed method performs relatively well.

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